Sequence Network Modeling for Unbalanced Fault Stability Analysis

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Solution Overview

Problem

Stability analysis in power grids with unbalanced topologies is challenging due to the need for complex calculus and frame conversions, especially in unbalanced systems where multiple coordinates are required to model positive, negative, and zero-sequence components.

Innovation Solution

A generalized dynamic circuit representation using the Laplace transform variable s is employed to translate voltage and current relationships into an interconnected sequence network with impedances in the Laplace domain, allowing direct conversion from a steady-state sequence network for stability analysis.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If dynamic phasor-based modeling is used to study asymmetry faults, then stability analysis can be performed, but tremendous efforts are required to deal with calculus and frame conversion

Engineering Contradiction:

Improvestability analysis capabilityVSAvoidmodeling complexity

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The patent replaces the complex dynamic phasor modeling approach (which requires calculus and frame conversion) with an impedance-based circuit modeling approach in the Laplace domain. This substitution eliminates the need for complex mathematical transformations while maintaining the ability to perform stability analysis under unbalanced conditions.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent transforms the modeling parameters from time-domain dynamic phasors to frequency-domain impedances in the Laplace domain. This parameter transformation simplifies the mathematical representation and enables straightforward stability analysis without requiring complex calculus operations or coordinate frame conversions.

Inventive Principle:

Principle #35Parameter changes

2Measurement precision

If multiple coordinates are used to model positive, negative, and zero-sequence components, then unbalanced systems can be accurately represented, but the analysis becomes significantly more complex

Engineering Contradiction:

Improveunbalanced system representation accuracyVSAvoidcoordinate transformation complexity

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

The patent merges the separate positive, negative, and zero-sequence network analyses into a unified impedance-based circuit model in the Laplace domain. By representing all sequence components through a common framework of impedances, the method maintains accurate representation of unbalanced conditions while eliminating the complexity of separate coordinate systems and their transformations.

Inventive Principle:

Principle #5Merging (Combining)

Data Source

PatentUS12468611B2Unified fault and stability analysis system and method considering unbalanced topologies

Publication Date: 2025.11.11 UNIV OF SOUTH FLORIDA

AI summary

For systems subject to unbalanced faults, analytical model building for stability assessment is a challenging task. This application presents a straightforward modeling approach. A generalized dynamic circuit representation is achieved by use of the Laplace transform variables. The voltage and current relationship at the fault location is translated into the relationship of three subsystems. The final circuit model is an interconnected sequence network with impedances in the Laplace domain. This circuit can be directly converted from a steady-state sequence network.